Gaming Die with Incongruent Sides and More Sides than Outcomes

ABSTRACT

This invention is a gaming die that use a combination of incongruent sides and a number of sides that is greater than the number of outcomes in order to produce practically fair results.

BACKGROUND

The present disclosure is generally directed to gaming dice, and moreparticularly to a gaming die that use a combination of incongruent sidesand a number of sides that is greater than the number of outcomes inorder to produce practically fair results.

Dice have been created that have incongruent sides and are practicallyfair, such as the 400 year old juryeonggu die from Korea. This is afourteen-sided, fourteen-outcome die used in a traditional drinkinggame. Additionally, there are a few examples of dice with incongruentsides in gaming, such as the Zocchi five-sided die described in U.S.Pat. No. 6,926,275.

Dice have also been created that have more sides than outcomes, such asthe four-outcome (d4), eight-sided (octahedron) die, or the ten-outcome(d10) twenty-sided die. The eight-sided d4 is of particular note becauseit is designed for the purpose of being more aesthetically pleasing thanthe traditional tetrahedron d4.

It would be useful to have dice that were aesthetically pleasing andfair, as well as simple and cheap to manufacture.

SUMMARY

In one example of a die with incongruent sides and more sides thanoutcomes according to this invention, the die is a “truncatedoctahedron” having fourteen sides. An octahedron is used as the baseshape, then the “points” are removed to create a shape with six squarefaces and six hexagonal faces. Outcomes are then assigned to the sidessuch that there are more sides than outcomes.

In another example of a die with incongruent sides and more sides thanoutcomes according to this invention, the die is a “chamfered cube”having eighteen sides. A cube is used as the base shape, then theintersections of edges are chamfered, or shaved down, to create a shapewith six square faces and twelve hexagonal faces. Outcomes are thenassigned to the sides such that there are more sides than outcomes.

These as well as other aspects, advantages, and alternatives, willbecome apparent to those of ordinary skill in the art by reading thefollowing detailed description, with reference where appropriate to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view of an example embodiment showing a truncatedoctahedron shape.

FIG. 2 is an isometric view of an example embodiment showing a truncatedoctahedron shape where the edge length of hexagonal sides differs fromthat of FIG. 1.

FIG. 3 is an isometric view of an example embodiment showing a chamferedcube shape.

FIG. 4 is an isometric view of an example embodiment showing a chamferedcube shape where the edge length of hexagonal sides differs from that ofFIG. 3.

FIG. 5 is an orthogonal view of an example embodiment showing atruncated octahedron shape labeled with six outcomes.

FIG. 6 is an orthogonal view of an example embodiment showing atruncated octahedron shape labeled with four outcomes.

FIG. 7 is an orthogonal view of an example embodiment showing atruncated octahedron shape labeled with eight outcomes.

FIG. 8 is an orthogonal view of an example embodiment showing atruncated octahedron shape labeled with ten outcomes.

FIG. 9 is an orthogonal view of an example embodiment showing achamfered cube shape labeled with twelve outcomes.

FIG. 10 is an orthogonal view of an example embodiment showing achamfered cube shape labeled with ten outcomes.

FIG. 11 is an orthogonal view of an example embodiment showing achamfered cube shape labeled with two outcomes.

DETAILED DESCRIPTION

In the particular embodiment illustrated in FIG. 1, hexacube die 50includes a die body 100, square sides 110, and hexagonal sides 120. Thedie body 100 is composed of plastic or another suitable material that issubstantially rigid and lightweight. Die body 100 can be shaped in itsfinal form and manufactured through a 3-D printing, plastic molding, orother suitable process. Die body 100 can also be shaped in anintermediate base form, such as a cube or octahedron, and reduced intoits final form by removing excess portions of material from the points.

Square sides 110 are substantially flat and substantially square shaped.The surface of square sides 110 can be imprinted with numbers, pipsrepresentative of numerical values, or other images as appropriate forthe intended use of hexacube die 50.

Hexagonal sides 120 are substantially flat and substantially hexagonshaped. As illustrated in FIG. 1, hexagonal sides 120 are shaped asirregular hexagons. The surface of hexagonal sides 120 can be imprintedwith numbers, pips representative of numerical values, or other imagesas appropriate for the intended use of hexacube die 50.

The term ‘incongruent sides’ refers to the fact that square sides 110have different surface areas and/or shapes than hexagonal sides 120. Dueto differences in surface area, shape, and edge length, square sides 110have a different probability of landing face down (and thus thecorresponding opposite side being face up) than hexagonal sides 120.

The term hexacube die′ as used in this document refers to a die that hasboth square and hexagonal sides. It should be noted that this inventiondoes not contemplate only hexacube dice with square and hexagonal sides,as other shapes may be constructed according to the principlesdiscussed, such as a chamfered octahedron which results in a die havingtwenty sides in the shape of triangles and hexagons.

To aid in determining fairness of a die, the hex to square ratio iscalculated as the length of an edge that is shared by hexagonal sides120 divided by the length of an edge of a square side 110. The Best Modehexacube illustrated in FIG. 1 has a hex to square ratio of 0.4044. Inthe labeled hexacube illustrated in FIG. 5, half of the square sides 110are assigned to an outcome of 1, half of the square sides 110 areassigned to an outcome of 6, and hexagonal sides 120 are distributedevenly among outcomes 2, 3, 4, and 5. For the Best Mode hexacubeillustrated in FIGS. 1 and 5, empirical testing has shown theprobability of any of square sides 110 landing face up on a given rollto be approximately 5.56%, while the probability of any of hexagonalsides 120 landing face up on a given roll is approximately 8.33%. Theodds of any of outcomes 1-6 landing face up on any given roll isapproximately 16.66%.

FIG. 2 illustrates a hexacube die 50 where the length of hexagonal sides120 is set such that hexagonal sides 120 appear nearly as triangles.

The shape of the die illustrated in FIG. 3 is a chamfered cube 60. Thiscan also be referred to as a tetratruncated rhombic dodecahedron, or(inaccurately) as a truncated rhombic dodecahedron. The base shape ofthis die is a cube, and the final shape as illustrated can be reached byremoving material at the intersections of edges (a process known aschamfering in woodworking or related arts). As with hexacube 50, thesides of chamfered cube 60 in its final shape are hexagonal or squareshaped. Chamfered cube 60 as illustrated in FIG. 3 has six square sides110 and twelve hexagonal sides 120. The hex to square ratio of chamferedcube 60 illustrated in FIG. 3, as calculated by the formula describedabove, is 0.5738. Chamfered cube 60 can be used as an approximately fairtwelve-sided die, or “d12”, by assigning each square side 110 adifferent outcome from 1-12, and then assigning each of the remainingoutcomes to two hexagonal sides 120, as illustrated in FIG. 9.

FIG. 4 illustrates a chamfered cube 60 where the length of hexagonalsides 120 differs from that of the chamfered cube 60 illustrated in FIG.3.

FIGS. 8 and 10 illustrate dice where the number of assigned outcomestotals ten. In many tabletop dice games, it is common to use a pair of“d10” or ten-outcome dice to generate a random number from 1-100 (a“percentile” roll), by assigning the result of one die to the “tens”digit of the final result and assigning the result of the second die tothe “ones” digit (and treating two tens or zeroes as a result of 100).The dice illustrated in FIGS. 8 and 10 are each labeled with tenoutcomes and are intended to be usable as a “d10” or “percentile” pair.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to those skilled in the art.The various aspects and embodiments disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims. Other embodimentsmay be utilized, and other changes may be made, without departing fromthe spirit or scope of the subject matter presented herein, for example,die body 100 can have a different shape, or a different number ofoutcomes may be assigned to the dice shapes previously described, suchas the four outcomes for a hexacube die shown in FIG. 6, eight outcomesshown in FIG. 7, or ten outcomes shown in FIG. 8. Also, additionalvariations are contemplated such as the alternate labeling of tenoutcomes for a chamfered cube die with eighteen sides shown in FIG. 10,or the two-outcome labeling for a chamfered cube die with eighteen sidesshown in FIG. 11. It will be readily understood that the aspects of thepresent disclosure, as generally described herein and illustrated in thefigures, can be arranged, substituted, combined, separated, and designedin a wide variety of different configurations, all of which arecontemplated herein.

What is claimed is:
 1. A gaming die comprising: a die body; a first sidehaving a first outcome; a second side having a second outcome; a thirdside having a third outcome; a fourth side having the first outcome;where the shape of at least one of the first, second, or third sides isdifferent from the shape of at least one of the first, second, or thirdsides.
 2. The gaming die of claim one wherein the die body has the shapeof a truncated tetrahedron.
 3. The gaming die of claim two wherein thedie body has the shape of a tetratruncated rhombic dodecahedron.